BREAKING: OpenAI ETH-Preprint (Oct 2026) claims subexponential #k-SAT • SHARPLOGIC.DEV • Exact deadlock & livelock counting for agent graphs • Free Offline Sentinel Key Active: ETH-2026 • In-Agent Python Middleware + Standalone CLI Available •  BREAKING: OpenAI ETH-Preprint (Oct 2026) claims subexponential #k-SAT • SHARPLOGIC.DEV • Exact deadlock & livelock counting for agent graphs • Free Offline Sentinel Key Active: ETH-2026 • In-Agent Python Middleware + Standalone CLI Available • 
● UNIVERSE // '26 :: SYSTEM TWO FORMAL VERIFICATION FOR AI AGENTS

COUNT THE TRAPS IN YOUR AI AGENTS.
EXACTLY.

Multi-agent graphs hide retry loops with no exit, dead-end nodes, and approval paths nobody traced. SharpLogic compiles your workflow graph into a CNF formula and counts β€” exactly β€” the condition assignments that leave it stuck (#F). Sparse workflow graphs resolve in microseconds; dense formulas take longer (exact counting is exponential in the worst case, up to the 64-variable engine limit).

πŸ”‘ ACCESS CODE: Fill username to claim Sentinel Token
⚑ INTEGRATE INTO YOUR AGENT (TWO NATIVE MODES):
from sharplogic import AgentGuard

# Local guardrail: exact deadlock/livelock audit of your workflow graph
# (0 cloud calls; the analysis runs entirely on your machine).
WORKFLOW = {
    "nodes": ["Tool_Executor", "Critic_Fallback", "Human_Approval_Gate"],
    "terminals": ["Human_Approval_Gate"],
    "edges": [
        {"from": "Tool_Executor", "to": "Critic_Fallback",
         "condition": "tool_timeout or execution_error"},
        {"from": "Critic_Fallback", "to": "Tool_Executor",
         "condition": "retry_prompt_generated and retry_count <= 3"},
        {"from": "Critic_Fallback", "to": "Human_Approval_Gate",
         "condition": "not retry_prompt_generated or retry_count > 3"},
    ],
}
guard = AgentGuard(token="YOUR_TOKEN", graph=WORKFLOW)

# Audit the whole graph: counts the condition assignments that trap it
report = guard.audit()
print(report["exact_count"])  # trap assignments (#F); 0 = no traps found

# Runtime check of one transition against the current conditions
guard.assert_safe("Critic_Fallback", "Tool_Executor",
                  state={"retry_prompt_generated": True}, retry_count=2)
πŸ”₯ VIRAL REFERRAL HUB: UNLOCK ADVANCED GUARDIAN TIERS
0 DEVELOPERS INVITED

Share your personalized invite code with colleagues to unlock the auto-patch tier and join the waitlist for upcoming tiers:

TIER 1 (ACTIVE)
Offline #k-SAT & Middleware
Local exact model-counting audits plus the runtime Python AgentGuard (full graph audit + per-transition checks).
TIER 2 (INVITE 1)
1-Click Auto-Patching
Synthesizes real blocking clauses from the solver’s counterexample assignments and re-counts #F exactly after each round β€” live in the sandbox above.
TIER 3 (INVITE 3)
GitHub Actions CI/CD β€” ROADMAP
Waitlist / roadmap β€” not yet shipped: a PR bot that fails checks when a workflow change introduces trap states. Unlocking records your waitlist spot.
TIER 4 (INVITE 5)
Sentinel Hall of Fame β€” ROADMAP
Planned β€” not yet live: contributor listing on the SharpLogic GitHub README and an SVG badge for top inviters.
langgraph_workflow_verifier.rs
🚨 192 CYCLIC DEADLOCKS DETECTED
[!] DEADLOCK CYCLE: Tool ⇄ Critic
User Goal
Entrypoint
β†’
Planner Agent
Decomposition
β†’
Tool Executor
API Invocation
⇄
Critic Fallback
Deadlock Trap
β†’
Human Gate
Never Reached
SATISFYING LOOPHOLE STATES (#F)
192
192 out of 1,048,576 execution trajectories trigger infinite retry loops between Tool Executor and Critic Fallback.
WORST-CASE MPE GHOST TRAJECTORYβ„’
[context_ambiguity=1] ∧ [tool_timeout=1] ∧ [retry_count>3]
β‡’ Under these conditions the agent can bounce between the two nodes with no enabled exit.
SOLVE TIME: measured live on every run
Demo scenarios are hand-authored benchmark formulas used to exercise the exact counting engine β€” they are not compiled from a user graph. Your own graphs are compiled from their actual topology and guard conditions.
01 / EXACT #k-SAT COUNTING

Exhaustive 2ⁿ Counting

A 20-variable formula has 1,048,576 assignments. 10,000 prompt evals sample under 1% of them. SharpLogic counts the satisfying assignments exactly β€” every one β€” with component decomposition and subproblem caching. Sparse workflow formulas resolve in microseconds; dense random formulas hit the exponential wall like every exact counter.

02 / MPE GHOST PATHβ„’

Exact Counterexamples

Instead of ambiguous probability scores, SharpLogic isolates the exact edge conditions where your agent crashes, loops infinitely, or bypasses human approval gates.

03 / FORMAL GUARDRAIL

Self-Synthesizing Patch

Once a trap is detected, SharpLogic synthesizes blocking clauses from the solver’s own counterexample assignments, generalizes them literal by literal, and re-counts #F exactly after every round. The reported patched count is the engine’s real recount β€” and the loop stops when it reaches 0 or the round budget ends.

FREQUENTLY ASKED QUESTIONS

Yes β€” in two modes: (1) In-Agent Middleware via from sharplogic import AgentGuard, which audits your whole workflow graph exactly and checks individual transitions against the current conditions at runtime; and (2) Standalone CLI (install.py), which audits exported LangGraph/Dify workflow JSON offline β€” graphs with up to 16 distinct condition atoms by exact enumeration; larger graphs go through the CNF engine in the full package.
A research claim published in October 2026 (expert review ongoing; not yet peer-reviewed) argues that exact #k-SAT counting can be done in subexponential time. SharpLogic does not implement that claimed algorithm. It uses a classical exact DPLL counter with component decomposition and caching, and compiles your multi-agent graph into a trap-counting formula whose satisfying assignments are exactly the condition assignments that deadlock or livelock the workflow.
No. The install.py script and the AgentGuard engine run 100% locally on your machine. Zero cloud API calls, zero prompt leaks, and $0 token cost.